Question: Simplify the following expression: $ q = \dfrac{-3}{10} + \dfrac{-6r - 8}{3r} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{3r}{3r}$ $ \dfrac{-3}{10} \times \dfrac{3r}{3r} = \dfrac{-9r}{30r} $ Multiply the second expression by $\dfrac{10}{10}$ $ \dfrac{-6r - 8}{3r} \times \dfrac{10}{10} = \dfrac{-60r - 80}{30r} $ Therefore $ q = \dfrac{-9r}{30r} + \dfrac{-60r - 80}{30r} $ Now the expressions have the same denominator we can simply add the numerators: $q = \dfrac{-9r - 60r - 80}{30r} $ $q = \dfrac{-69r - 80}{30r}$